Noncommutative multi-instantons on R-2n x S-2

Abstract

Generalizing self-duality on R-2 x S-2 to higher dimensions, we consider the Donaldson-Uhlenbeck-Yau equations on R-2n x S-2 and their noncommutative deformation for the gauge group U(2). Imposing SO(3) invariance (up to gauge transformations) reduces these equations to vortex-type equations for an Abelian gauge field and a complex scalar on R-theta(2n). For a special S-2-radius R depending on the noncommutativity theta we find explicit solutions in terms of shift operators. These vortex-like configurations on R-theta(2n) determine SO(3)-invariant multi-instantons on R-theta(2n) x S-R(2) for R = R(theta). The latter may be interpreted as sub-branes of codimension 2n inside a coincident pair of noncommutative Dp-branes with an S-2 factor of suitable size